Machine Design and Computer Integrated Manufacturing (CIM) closes out Part B2 (Mechanical) of the GATE Robotics and Automation (RA) 2027 paper. Its design half is driven by a few decisive tools — the factor of safety, the failure theories, the endurance limit, and the shaft/element sizing formulas — while the CIM half covers CAD/CAM, CNC and additive manufacturing. This guide reviews the design essentials and works through five GATE-style problems in full.
TABLE OF CONTENTS
Factor of safety & static loading
The factor of safety (FoS) is the ratio of a material’s strength to the working (design) stress, and it captures the margin against failure. For ductile materials the yield strength is used; for brittle materials the ultimate strength. A larger FoS is safer but heavier and costlier, so design balances the two.
Theories of failure
Under combined stresses, a failure theory predicts the onset of yielding. The two examined most are the maximum-shear-stress (Tresca) theory, which says failure occurs when the maximum shear reaches σy/2, and the distortion-energy (von Mises) theory, which uses an equivalent stress. Von Mises is less conservative and matches ductile metals well.
Fatigue & the endurance limit
Components under fluctuating load fail by fatigue at stresses well below the static strength. The S–N diagram plots stress amplitude against cycles to failure; for steels it flattens at the endurance limit, often approximated as Se ≈ 0.5×Sut. The Goodman and Soderberg lines combine mean and alternating stress for safe design.
Machine elements (shafts)
Shafts, keys, bolts, gears, springs and bearings are sized from stress limits. For a solid circular shaft transmitting torque T, the shear stress is τ = 16T/(πd³), which is inverted to find the required diameter for a given allowable stress. Combined bending and torsion use the equivalent-torque and equivalent-moment approach.
CAD/CAM, CNC & additive manufacturing
The CIM half integrates design and manufacturing: CAD models geometry, CAM generates tool paths, and CNC machines execute them from G-code. Additive manufacturing (3-D printing) builds parts layer by layer. Typical questions cover interpolation, NC coordinate systems, and the trade-offs between subtractive and additive processes.
Worked examples (GATE-style)
Example 1 — factor of safety
A ductile component has a yield strength of 250 MPa and operates at a working stress of 100 MPa. Find the factor of safety.
Solution. FoS = σy/σworking = 250/100 = 2.5.
Example 2 — von Mises stress
At a point the principal stresses are σ1 = 100 MPa, σ2 = 50 MPa, σ3 = 0. Find the von Mises equivalent stress.
Solution. σvm = √(½[(100−50)² + (50−0)² + (0−100)²]) = √(½[2500 + 2500 + 10000]).
= √7500 = 86.6 MPa.
Example 3 — endurance limit
A steel has an ultimate tensile strength of 600 MPa. Estimate its endurance limit.
Solution. For steels, Se ≈ 0.5×Sut = 0.5×600 = 300 MPa (before applying surface, size and load correction factors).
Example 4 — shaft diameter from torque
A solid shaft must transmit 500 N·m with an allowable shear stress of 40 MPa. Find the minimum diameter.
Solution. d³ = 16T/(πτ) = 16×500/(π×40×10⁶) = 8000/(1.257×10⁸) = 6.366×10−5 m³.
d = (6.366×10−5)1/3 = 0.0399 m = 39.9 mm (use 40 mm).
Example 5 — maximum-shear-stress theory
A ductile material has a yield strength of 250 MPa. According to the maximum-shear-stress (Tresca) theory, at what shear stress does it yield?
Solution. Tresca predicts yielding when τmax = σy/2 = 250/2 = 125 MPa.
Key formulas
FORMULA SHEET
FoS: σy/σworking (ductile)
Tresca: τmax = σy/2
von Mises: σvm = √(½[(σ1−σ2)²+(σ2−σ3)²+(σ3−σ1)²])
Endurance: Se ≈ 0.5 Sut
Shaft: τ = 16T/(πd³), d = [16T/(πτ)]1/3
Common mistakes to avoid
- Using ultimate strength for ductile FoS — ductile design uses the yield strength, brittle design the ultimate.
- Forgetting the ½ inside the von Mises root, or squaring the differences incorrectly.
- Applying the raw 0.5×Sut endurance limit without the surface, size and reliability correction factors in a full design.
- Cube-root slips when solving for shaft diameter — keep the units in metres and take the cube root last.
- Mixing Tresca and von Mises — Tresca is the more conservative (safer) of the two.
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Frequently asked questions
What is the factor of safety?
The factor of safety is the ratio of a material’s strength to the actual working stress. It provides a margin against uncertainties in load, material and analysis — a FoS of 2.5 means the component can carry 2.5 times its design stress before yielding.
When should I use von Mises versus Tresca?
Both predict yielding of ductile materials. Tresca (maximum shear) is simpler and more conservative; von Mises (distortion energy) is more accurate and less conservative, and is generally preferred for ductile metals under combined loading.
Why do parts fail by fatigue below their static strength?
Repeated (cyclic) loading initiates and grows microscopic cracks over many cycles, so a component can fail at a stress far below its static strength. The endurance limit, about half the ultimate strength for steels, is the stress below which steel can endure effectively infinite cycles.
This solved-problems guide is part of the complete GATE RA 2027 Syllabus overview. For the full topic breakdown, see the Machine Design and CIM syllabus guide.
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